The formula for the final amount (A) in simple interest is P * (1 + R * T), where P is the principal, R is the annual interest rate, and T is the time in years. Given: A = $3,937, R = 4.5% = 0.045, T = 6 years. Substitute the values into the formula: $3,937 = P * (1 + 0.045 * 6) Calculate the product of R and T: 0.045 * 6 = 0.27 Add 1 to the product: 1 + 0.27 = 1.27 So, $3,937 = P * 1.27 To find P, divide the amount by 1.27: P = $3,937 / 1.27 P = $3,100 Why others are wrong: A — Correct calculation. B — This is the simple interest earned (Amount - Principal = $3937 - $3100 = $837), not the principal. C — This results from an incorrect calculation ($3937 * (1 - 0.27) = $2874), wrongly assuming interest is subtracted from the final amount. D — This results from incorrectly dividing the final amount by only (R * T) ($3937 / (0.045 * 6) = $14,581.48), omitting the '1' in the (1 + RT) part of the formula.

1. The formula for the total Amount (A) in simple interest is A = P(1 + RT), where P is the Principal, R is the annual interest rate (as a decimal), and T is the time in years. 2. Given A = $12,600, R = 7% = 0.07, and T = 3 years. 3. Substitute the values into the formula: $12,600 = P(1 + 0.07 * 3). 4. Calculate the term inside the parenthesis: 1 + 0.21 = 1.21. 5. So, $12,600 = P(1.21). 6. To find P, divide the Amount by 1.21: P = $12,600 / 1.21. 7. P ≈ $10,413.22. Why others are wrong: A — Correct. B — This results from incorrectly calculating the simple interest based on the *Amount* ($12,600 * 0.07 * 3 = $2,646) and then subtracting this from the Amount ($12,600 - $2,646 = $9,954). C — This results from incorrectly calculating the principal by dividing the Amount by (1 + R), effectively ignoring the time (T) component ($12,600 / (1 + 0.07) = $12,600 / 1.07 ≈ $11,775.70). D — This results from an iterative calculation where interest is mistakenly subtracted from the *decreasing balance* each year, rather than using the original principal for all interest calculations ($12,600 - (12,600 * 0.07) = $11,718; $11,718 - (11,718 * 0.07) = $10,897.74; $10,897.74 - (10,897.74 * 0.07) = $10,134.90).

1. The formula for simple interest is I = PRT, where I is Interest, P is Principal, R is Rate, and T is Time. 2. Given values are: I = $750, P = $5,000, R = 6% or 0.06 per annum. 3. To find the Time (T), rearrange the formula: T = I / (P * R). 4. Substitute the given values into the formula: T = $750 / ($5,000 * 0.06). 5. Calculate the product of Principal and Rate: $5,000 * 0.06 = $300. 6. Now, divide the Interest by this product: T = $750 / $300. 7. T = 2.5 years. Why others are wrong: A — This result would be obtained if the annual interest rate was incorrectly assumed to be 10% (0.10) instead of 6%. (T = 750 / (5000 * 0.10) = 1.5). B — This is the correct calculation. C — This result would be obtained if the annual interest rate was incorrectly assumed to be 5% (0.05) instead of 6%. (T = 750 / (5000 * 0.05) = 3). D — This result could occur from significant miscalculation, for instance, if the annual interest was mistakenly calculated as $150 ($5,000 * 0.03, implying a 3% rate) and then $750 / $150 = 5 years.

1. First, calculate the original principal (P) by subtracting the accrued interest from the total value: P = Total Value - Interest. 2. P = £12,075 - £1,575 = £10,500. 3. Identify the given interest (I = £1,575) and time (T = 3 years). 4. Use the simple interest formula: I = P * R * T, where R is the annual interest rate as a decimal. 5. Rearrange the formula to solve for R: R = I / (P * T). 6. Substitute the values: R = £1,575 / (£10,500 * 3). 7. Calculate R: R = £1,575 / £31,500 = 0.05. 8. Convert the decimal rate to a percentage: R = 0.05 * 100% = 5.0%. Why others are wrong: A — Results from an arithmetic error in calculating the principal or applying the interest rate formula. B — Results from an arithmetic error in calculating the principal or applying the interest rate formula. D — Results from an arithmetic error in calculating the principal or applying the interest rate formula.

The formula for simple interest is SI = P * R * T, where SI is simple interest, P is principal, R is annual interest rate (as a decimal), and T is time in years. Given: SI = $560, R = 3.5% = 0.035, T = 4 years. To find P, rearrange the formula: P = SI / (R * T). Substitute the given values: P = $560 / (0.035 * 4). Calculate the product of R and T: 0.035 * 4 = 0.14. Now, divide the simple interest by this product: P = $560 / 0.14. P = $4000. The initial principal amount invested was $4000. Why others are wrong: A — Correct calculation based on the simple interest formula. B — This results from incorrectly applying the formula as SI * T / R ($560 * 4 / 0.035). C — This results from incorrectly applying the formula as SI * R * T ($560 * 0.035 * 4), as if SI itself were the principal. D — This results from an incorrect conversion of the interest rate, treating 3.5% as 0.35 instead of 0.035 ($560 / (0.35 * 4)).